The reason it's not working is that a few years ago Google
deprecated the authentication process that Live Writer uses, i.e.
Google declared it as obsolete because it is not secure enough for the
modern web, and developers should stop using it ASAP. Unfortunately
Live Writer was not updated to use the new more secure OAuth
2 standard. Google removed support for it back in about May this year,
then temporarily re-enabled it for Blogger / WLW, now it looks like they
have pulled it for good.

It's not straightforward to fix, certainly more than a couple of
lines of code. If you want to comment, please post to the GitHub issue
via the link above, as that will be read by the developers. They
will not generally be following the MS forums as it's
no longer an MS product.

This could not have happened at a worse time given how many bloggers
rely on the holiday season for income. It seems that Google has taken
the release of this product as a green light to finally deprecate the
legacy auth leaving Blogger users stranded.

Credits

Why this? It is the simple blog of a Last Exile fan and is intended to express the enjoyment we derive from studio Gonzo's production. Although we closely relate with those characters, we aren't them in real life. We just want to keep the memory of these incredible young kids alive. So go buy Gonzo's Last Exile DVD's!